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Rev. Lett."],"accepted":{"date-parts":[[2026,7,27]]},"abstract":"<jats:p>\n                    This Letter presents a lattice quantum chromodynamics (QCD) determination of\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <a:mi>\u03c0<\/a:mi>\n                      <a:mi>\u03c0<\/a:mi>\n                      <a:mi>\u03c0<\/a:mi>\n                    <\/a:math>\n                    scattering amplitudes for the isospin-2 channel with angular momentum and parity\n                    <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <c:msup>\n                        <c:mi>J<\/c:mi>\n                        <c:mi>P<\/c:mi>\n                      <\/c:msup>\n                      <c:mo>=<\/c:mo>\n                      <c:msup>\n                        <c:mn>1<\/c:mn>\n                        <c:mo>+<\/c:mo>\n                      <\/c:msup>\n                    <\/c:math>\n                    . The calculation is performed using unphysically heavy light-quark masses, corresponding to a pion mass of\n                    <e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <e:msub>\n                        <e:mi>m<\/e:mi>\n                        <e:mi>\u03c0<\/e:mi>\n                      <\/e:msub>\n                      <e:mo>\u2248<\/e:mo>\n                      <e:mn>400<\/e:mn>\n                      <e:mtext>\u2009<\/e:mtext>\n                      <e:mtext>\u2009<\/e:mtext>\n                      <e:mi>MeV<\/e:mi>\n                    <\/e:math>\n                    , for which the\n                    <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <g:mi>\u03c1<\/g:mi>\n                    <\/g:math>\n                    meson manifests as a narrow resonance. The analysis employs a previously developed formalism that nonperturbatively relates the finite-volume spectra of two- and three-pion systems to their infinite-volume scattering amplitudes. We combine earlier lattice QCD results for\n                    <i:math xmlns:i=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <i:mi>\u03c0<\/i:mi>\n                      <i:mi>\u03c0<\/i:mi>\n                    <\/i:math>\n                    systems with isospins 1 and 2 with new determinations of the isospin-2 three-pion finite-volume spectrum, obtained for three cubic, periodic lattice volumes with box length ranging from\n                    <k:math xmlns:k=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <k:mo>\u2248<\/k:mo>\n                      <k:mn>4<\/k:mn>\n                      <k:mo>\/<\/k:mo>\n                      <k:msub>\n                        <k:mi>m<\/k:mi>\n                        <k:mi>\u03c0<\/k:mi>\n                      <\/k:msub>\n                    <\/k:math>\n                    to\n                    <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <m:mn>6<\/m:mn>\n                      <m:mo>\/<\/m:mo>\n                      <m:msub>\n                        <m:mi>m<\/m:mi>\n                        <m:mi>\u03c0<\/m:mi>\n                      <\/m:msub>\n                    <\/m:math>\n                    . These combined data constrain the low-lying partial waves of the infinite-volume three-pion\n                    <o:math xmlns:o=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <o:mrow>\n                        <o:mi>K<\/o:mi>\n                      <\/o:mrow>\n                    <\/o:math>\n                    matrix, from which we solve a set of coupled integral equations to extract the corresponding scattering amplitudes.\n                  <\/jats:p>","DOI":"10.1103\/yyfr-j1yl","type":"journal-article","created":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T16:31:02Z","timestamp":1785169862000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Isotensor\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <mml:mi>\u03c0<\/mml:mi>\n                      <mml:mi>\u03c0<\/mml:mi>\n                      <mml:mi>\u03c0<\/mml:mi>\n                    <\/mml:math>\n                    Scattering with a\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <mml:mi>\u03c1<\/mml:mi>\n                    <\/mml:math>\n                    -Resonant Subsystem from QCD"],"prefix":"10.1103","volume":"137","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1109-1473","authenticated-orcid":true,"given":"Ra\u00fal A.","family":"Brice\u00f1o","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01an7q238","id-type":"ROR","asserted-by":"publisher"}],"name":"University of California"},{"id":[{"id":"https:\/\/ror.org\/02jbv0t02","id-type":"ROR","asserted-by":"publisher"}],"name":"Lawrence Berkeley National Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9184-8354","authenticated-orcid":true,"given":"Maxwell 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propagate their uncertainties, which are subdominant to the uncertainties from three-pion finite-volume energies.","type":"other"},{"key":"yyfr-j1ylCc179R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.103.114502","type":"journal-article"},{"key":"yyfr-j1ylCc180R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.105.054509","type":"journal-article"},{"key":"yyfr-j1ylCc181R1","unstructured":"The scheme-dependence emerges due to a necessary choice of cutoff function for the integral equations and a parametrization of the two-body K matrix.","type":"other"},{"key":"yyfr-j1ylCc182R1","unstructured":"The dipion invariant mass is related to the third pion momentum via M\u03c0\u03c02=E2+m\u03c02\u22122Em\u03c02+k2, with similar expression for M\u03c0\u03c0\u2032 in terms of k\u2032.","type":"other"},{"key":"yyfr-j1ylCc183R1","unstructured":"This is also apparent in Fig.\u00a01 where the lattice QCD-computed energies are inconsistent with the energies from a parametrization where K3=0.","type":"other"},{"key":"yyfr-j1ylCc184R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP03(2024)048","type":"journal-article"},{"key":"yyfr-j1ylCc185R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.56.3057","type":"journal-article"},{"key":"yyfr-j1ylCc186R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.59.074001","type":"journal-article"},{"key":"yyfr-j1ylCc186R2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.60.099906","type":"journal-article"},{"key":"yyfr-j1ylCc186R3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.75.099903","type":"journal-article"},{"key":"yyfr-j1ylCc187R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.65.054009","type":"journal-article"},{"key":"yyfr-j1ylCc188R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.97.242002","type":"journal-article"},{"key":"yyfr-j1ylCc189R1","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP12(2021)038","type":"journal-article"},{"key":"yyfr-j1ylCc190R1","doi-asserted-by":"publisher","DOI":"10.1103\/6nql-yrhw","type":"journal-article"},{"key":"yyfr-j1ylCc191R1","unstructured":"For example, using fit 1 in Table\u00a0II of the Supplemental Material, one finds a nonzero value of K3. After varying the choice of the parametrization, K3 becomes consistent with 0.","type":"other"},{"key":"yyfr-j1ylCc192R1","unstructured":"www.exohad.org.","type":"other"},{"key":"yyfr-j1ylCc193R1","unstructured":"www.dirac.ac.uk.","type":"other"},{"key":"yyfr-j1ylCc194R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysbps.2004.11.254","type":"journal-article"},{"key":"yyfr-j1ylCc195R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2010.05.002","type":"journal-article"},{"key":"yyfr-j1ylCc196R1","unstructured":"R. Babich, M.\u2009A. Clark, and B. Joo, in SC 10 (Supercomputing 2010) New Orleans, Louisiana (IEEE Computer Society, Washington, DC, 2010), 10.1109\/SC.2010.40.","type":"other"},{"key":"yyfr-j1ylCc197R1","doi-asserted-by":"publisher","DOI":"10.5555\/3014904.3014995","type":"conference-proceedings","volume-title":"Proceedings of SC 16 (Supercomputing 2016) Salt Lake City, Utah","author":"K. Clark","year":"2016"},{"key":"yyfr-j1ylCc198R1","volume-title":"Supercomputing","author":"B. Jo\u00f3","year":"2013","type":"book"},{"key":"yyfr-j1ylCc199R1","unstructured":"B. Jo\u00f3, mg_proto: A multigrid library for QCD, https:\/\/github.com\/JeffersonLab\/mg_proto\/.","type":"other"},{"key":"yyfr-j1ylCc200R1","doi-asserted-by":"publisher","DOI":"10.1145\/3592979.3593409","type":"journal-article"},{"key":"yyfr-j1ylCc201R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.105.201602","type":"journal-article"},{"key":"yyfr-j1ylCc202R1","volume-title":"Platform for Advanced Scientific Computing","author":"J. Chen","year":"2023","type":"book"}],"container-title":["Physical Review Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/yyfr-j1yl","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/yyfr-j1yl\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T15:24:23Z","timestamp":1788881063000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/yyfr-j1yl"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,8]]},"references-count":204,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2026,9]]}},"URL":"https:\/\/doi.org\/10.1103\/yyfr-j1yl","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2510.24894","asserted-by":"subject"}]},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,8]]},"assertion":[{"value":"2025-11-18","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"111901"}}